Doubly refracting crystal arrangement for reducing apertural defects

ABSTRACT

Arrangement of doubly refracting crystals for reducing apertural defects characterized in that there is added to a double refracting crystal a second double refracting crystal having the same geometrical form but having an opposite sign of double refraction, the optical axis of the second crystal being located in the plane defined by the system axis and the optical axis of the first crystal.

OR 3,64 ,018 vi p unllefl male [151 3,644,018 Pasold 1 51 Feb. 22, 1972 [s41 DOUBLY REFRACTING CRYSTAL 3,497,831 2/1970 Hickey et a1. ..350/150 x ARRANGEMENT FOR REDUCING 3,430,048 2/1969 Rubinstein ..350/157 UX APERTURAL DEFECTS 2,777,360 1/ 1957 Blaisse ..350/ 157 X [72] inventor: Gunter Paaold, Dresden, Germany OTHER PUBLICATIONS [73] Assignee: Veb Kombinat Robotron, Radeberg, Ger- Habegger, Astigmatic Aberration Correction lBM Tech.

many Discl. Bull. Vol. 11 No. 12 (May 1969) p. 1776. [22] Filed: Mar. 24, 1970 211 Appl. No.: 22,202

Primary Examiner-David Schonberg Assistant Examiner-Paul R. Miller Attorney-None and Nolte [52] US. Cl. ..350/l57, 350/147, 350/175 DR,

- 350/1310. 2 [571 ABSTRACT [51] Int. Cl. ..G02b 5/30 Arrangcmem of doubly raft-acting crysmls for reducing ape; [58] Field oISearch ..350/l47, 157, 175 DR, DIG. 2 mm] defects characterized in that there is added to a deuble refracting crystal a second double refracting crystal having the [56] Rehrm cued same geometrical form but having an opposite sign of double UNITED STATES PATENTS refraction, the optical axis of the second crystal being located g in the plane defined by the system axis and the optical axis of 3,497,284 2/1970 Kosanke et a1. ..350/150 the fir t crysmL 3,391,972 7/1968 Harris et al. ....350/150 3,503,670 3/1970 Kosanke et a1. ..350/ 150 5 Claims, 6 Drawing Figures n 1 e2 o2 I 1 d2 PATENTEDFEBZZ I972 SHEEI 1 BF 3 .w/vzsP 245010 DOUBLY REFRACTING CRYSTAL ARRANGEMENT FOR REDUCING APERTURAL DEFECTS This invention relates to an arrangement of doubly refracting crystals for reducing aperture aberrations, as for instance in digital light deflecting systems.

A doubly refracting crystal generally splits a light ray bundle into an ordinary and an extraordinary light ray bundle. Each of the divided light ray bundles gives rise to an image surface plane which in consequence of the resultant image errors exists not as a sharply defined point but rather as a blurred cluster of points or spot. It is a general requirement that size of the image spot be kept as small as possible in order that a clear, i.e., unblurred image be obtained.

In order to arrive at a situation wherein the image spots produced for each divided light ray bundle are kept as small as possible, all of the image defects of the doubly refracting crystals must be reduced as low as possible. The image defects arise from the bending of the light rays, or, light ray bundles, from the difference in path length distance between the ordinary and the extraordinary divided light ray bundles and the apertural defects of the doubly refracting crystals. An apertural defect can produce a picture or image spot of the same size as that due to the bending, i.e., difference in path length.

The basic or essential cause of the aforesaid is to be attributed to the finding that for the extraordinary divided light ray bundle, the focus points of the paraxial rays for different incident planes do not converge. The greatest aberration exists between the focus point of the paraxial rays for the incident plane which converges with the principal section of the doubly refracting crystals and the focus point for the incident plane which is perpendicular to the principal section.

A correction of the bending or deviation is not possible. A correction of the path length differences can be carried out by numerous known proposals. For example, for a doubly refracting crystal which is formed as a planoparallel plate, the correction is obtained by adding to such a crystal having either a positive or negative double refraction and additional similar crystal which is characterized by the opposite sign, i.e., negative or positive double refraction. The path length differences have in both of the crystals a different sign (positive or negative). By appropriate selection of the thickness of the second crystal, the path length difference can be made equal to zero.

In accordance with a further known possibility of correction of the path length difference, there is added to a doubly refracting crystal which is formed as a planoparallel plate, a further crystal which, however, in rotated by 90 from the optical axis of the first crystal. Each divided ray bundle then passes through one of the crystals as an ordinary divided ray bundle and through the other crystal as an extraordinary divided ray bundle. The total optical path length is therefore the same or equal for both of the divided ray bundles.

Special difficulties are encountered for the correction of apertural defects of doubly refracting crystals because the defect arises only in connection with the extraordinary divided ray bundle and apart from this depends ofthe azimuth angle of the incident plane. Firstly, in the use of doubly refracting crystal systems in which through multiple ray divisions many divided ray bundles are developed, the aperture defect is different for each divided ray bundle and, therefore, must be corrected individually by means of isotropic nonrotationally symmetrical lenses. On this basis, without resorting to a high expenditure, the required correction of the apertural defect cannot be carried out.

The object of the instant invention is to provide means for reducing the size of the image spot of extraordinary divided ray bundles due to the aperture defects of doubly refracting crystals with the smallest expense possible.

It is another object of the invention to reduce the size of the image spots of extraordinary divided raybundles due to the apertural defects of doubly refracting crystals by means which are not tedious and difficult to install and operate.

It is still another object of the invention to superpose for the extraordinary divided ray bundles. the focus point of the paraxial rays for the incident plane which coincides with the principal section of the doubly refracting crystals with the focus point of the incident plane which is perpendicular to the principal section. 1

These and other objects and advantages will become apparent from the consideration of the following disclosure.

According to a first embodiment of the invention, the above objects are realized by adding to any doubly refracting crystal. a second doubly refracting crystal of the same geometrical form, but characterized by an opposite sign of double refraction, the optical axis of the second crystal being located in the plane which is determined by the axis of the system and the optical axis of the first crystal. A parameter for one of the two crystals is established from the relationship or equation valid for the aforesaid arrangement and namely path length difference of the paraxial rays of the extraordinary divided ray bundle for the principal section equals path length difference of the section perpendicular to the principal section. By the term axis of the system" is meant the optical axis of the crystal arrangement.

The parameters of each of the doubly refracting crystals are characteristic of the basic form of construction and the dimensions thereof, for example the radius of curvature of the lenses or the thickness of the planoparallel plates, the ordinary and extraordinary refractive index and the angle between the optical axis and the system axis.

The arrangement in accordance with the invention of the doubly refracting crystal results in a marked reduction of aperture defects in connection with which a correction of the path length differences between ordinary and the extraordinary divided ray bundles has not at this time been taken into consideration.

In accordance with a further development of the invention, a simultaneous correction of the path length difference can be carried out by establishing a total of any two parameters of one of the crystals or any one parameter of each of the two crystals based on the aforementioned relationship. under consideration of an additional relationship valid for this arrangement. This further relationship constitutes the following: path length difference of the paraxial rays of the ordinary divided ray bundles equals path length difference of the paraxial rays of the extraordinary divided ray bundles for the principal section.

Preferably, the doubly refracting crystals of the arrangement according to the invention are developed as planoparallel plates and the thickness and angle between the optical axis of one of the crystals or the thickness of one of the crystals and the indicated angle of one of the other of the crystals are established from equations I and II (infra). These equations are formulated by establishing the above two relationships for a given arrangement in which a doubly refracting crystals are planoparallel plates.

According to a further embodiment of the invention, the problem of apertural defects is solved by adding to any one double refracting crystal anadditional completely identical crystal which, however, is rotated by with respect to the axis of the system and by including between the aforesaid two crystals an element which is capable of rotating the polarization plane of the divided ray bundle.

The term system axis as used herein is intended to designate the optical axis of the crystal arrangement.

It has been found advantageous to replace each of the two crystals by an identical system of doubly refracting crystals in which in each of the systems the path length difference between the ordinary and the extraordinary divided ray bun dles has been corrected as then the total image defect can be kept smaller than if individual crystals are used.

Both in the use of individual crystals and of systems it is advantageous to construct the doubly refracting crystals as planoparallel plates as this permits a particularly simple crystal arrangement.

The arrangement in accordance with the invention formed of 'two crystals or systems, has as compared toa single crystal or system, changed optical properties, such as, for instance, a

change in the distances or of the angles between the divided ray bundles. lf such a change is not desirable, a correction of the respective geometric measurements of the doubly refracting crystals can be carried out to thereby restore the original properties without disturbingly influencing or otherwise adversely affecting the required reduction of aperture defects. For example, if the double refracting crystals of the arrangement according to the invention are constructed as planoparallel plates then there results a {Tfold light devia tion.

if the thickness of all of the doubly refracting crystals are reduced to m then the same amount or change in light deviation is brought about as would be caused by a single crystal or system of unreduced crystal thickness.

The rotation of the polarization plane of the divided ray bundles by 90 is required in accordance with the invention can be achieved in a simple manner by means of a A/Z-thin plate.

The arrangements in accordance with the invention corresponding to the first and second embodiments as above set out have the effect that the extent or degree of the image spot caused by the aperture defect of the doubly refracting crystals or systems is reduced to a minimum. This reduction can amount to more than one order of magnitude. Any remaining apertural defect is their in the order of magnitude of the respective isotropic materials.

The substantial reduction of the size of the image spot of each of the divided ray bundles makes it possible to concentrate the image spots, i.c., to cause them to become more densely positioned (form a clearly defined point) then would be possible in an uncorrected doubly refracting crystal, or system. if the arrangement in accordance with the invention is used in a digital light deflecting system for the control of optical data storage or retention then the total number of divided ray bundles can be increased while the storage surface remains the same thereby increasing the total capacity of the device.

The invention, both its construction, and its method of operation, together with additional objects and advantages thereof, will be best understood from the following detailed description of certain specific embodiments with reference to the accompanying drawings in which:

FIG. 1 is a side elevation of an arrangement according to the invention with one positive and one added negative double refracting crystal;

H0. 2 is a side elevation of an arrangement according to the invention with two completely identical doubly refracting crystals;

FIG. 3 is a plan view ofFlG. 2;

H6. 4 is a side elevation of an arrangement according to the invention with two identical systems of doubly refracting crystals; and I FIG. 5 is a plan view of H6. 4;

HO. 6 is a light deflection system of two stages.

FIG. 1 refers to the first embodiment and FIGS. 2-5 to the second embodiment of the invention.

in all of the figures, the doubly refracting crystals are constructed as planoparallel plates.

The arrangement in accordance with the invention as hereinafter described, is considered a preferred construction. In this arrangement, there is added to a first and doubly refracting crystal 1, a second doubly refracting crystal 2. Both crystals 1 and 2 are constructed as planoparallel plates and their optical axes 3,4 and the system axis 5 are located in single plane. The thickness d; of crystal 2 and the angle 7 between the optical axis 4 and the system axis 5 can be established from equations l and ll (equations l and ll are set out in the table entitled Summary of Formula" given at the end of the description). There are given for the illustrated embodiment the thickness d, and the angle y, between the optical axis 3 and system axis 5. the ordinary refractive index n and the extraordinary refractive index n,., of crystal 1, as well as the ordinary refractive index m and the extraordinary refractive index n,. ofcrystal 2.

The doubly refracting crystal 1 splits a light ray bundle into an ordinary and extraordinary divided ray bundle. As the optical axis 4 of crystal 2 is located in a plane determined by the system axis 5 and optical axis 3 of crystal 1, the ordinary divided ray bundle also passes through crystal 2 as a ordinary divided ray bundle. The same is also true for the extraordinary divided ray bundle. Due to aperture defects, the focus points of the paraxial rays of the extraordinary divided ray bundles for any two incident planes of crystal 1 do not coincide.

A similar difference in positioning of the focus points due to aperture defects is also caused by crystal 2, however, this takes place in a opposite direction, i.e., with opposite signs as the double refraction of the two crystals 1 and 2 are distinguished by their sign. By establishing the thickness d, or the angle 'y, of a crystal 2 in accordance with equation I, it is assured that the difference in the positioning of the focus points which has developed between the two crystals 1 and 2 remains the same size regardless whether equation ll has or has not been taken into consideration. The resulting difference in position is therefore zero and thus in this arrangement the focus point of the paraxial rays of the extraordinary divided ray bundles coincide for any incident plane. As a result, an exact correction has been obtained for the paraxial rays and, furthermore, there has been obtained for any rays of the extraordinary divided ray bundles a considerable reduction of the aperture defect of the doubly refracting crystal.

If, as indicated, in the instant embodiment for establishing the thickness d, and the angle 7 of crystal 2, equation I1 is taken into consideration, in addition to equation I, then the correction of the path length difference between the ordinary and extraordinary ray bundle is realized in addition to the reduction of the aperture defect.

The arrangement shown in FIGS. 2 and 3 consists of a doubly refracting crystal 6 to which there has been added an entirely identical crystal 7 with the exception however, that it is rotated about the system axis by Between the two crystals 6 and 7 there is arranged a A/2-thin plate or lamina 8 for the rotation by 90 of the polarization plane of the divided ray bundles.

in FIGS. 4 and 5, there is shown an arrangement in which instead ofindividual crystals 6 and 7 there are used two identical systems 9 and 10 consisting each of doubly refracting crystals 6, ll or 7, 12. The position of the optical axis 13 in relation to 14 in system 9 and axis 14 in relation to 16 in system 10 coincide, i.e., are the same.

The doubly refracting crystals ll, 12 bring about, in the known manner, a correction of the path length difference between the ordinary and the extraordinary divided ray bundles. These crystals are rotated by 90 about the system axis in relation to the doubly refracting crystals 6,7 respectively, so that the position of the optical axis 14 and 16 relative to the system axis 5 is not changed. The doubly refracting crystal 6 splits an occurring converging light ray bundle into an ordinary and an extraordinary divided ray bundle. Both of the resultant divided ray bundles are laterally offset in relation to each other. The focus point of their paraxial rays are not in the same plane due to the path length differences existing between the ordinary and the extraordinary divided ray bundles.

The ordinary divided ray bundle thereafter passes through the doubly refracting crystal 11 as an extraordinary divided ray bundle and the extraordinary divided ray bundle pass through the crystal 11 as an ordinary divided ray bundle due to the fact that the crystal 11 is rotated in relation to crystal 6 by 90 about the system axis. The path length difference between the divided ray bundles is equalized in crystal 11, as a result of which the two focus points are now in one plane.

However, because of the aperture defects, the focus points of the paraxial rays for the two divided ray bundles for different incidence planes do not coincide and the image spots which are produced by such system 9 still exhibit a considerable size. The largest deviation occurs between the focus points of the paraxial rays for the incident plane which incident plane coincides with the principal section of the doubly refracting crystal 6 and the focus points for the incident plane which is perpendicular to this principal section.

Since, however, in accordance with the invention, the system is rotated about the system axis 5 and the polarization plane of both divided ray bundles is rotated by 90 by the A/Z-thin plate 8, the incident plane which coincides with the principal section of crystal 6 is disposed perpendicular to the principal section of crystal 7. An incident plane which is perpendicular to the principal section of crystal 6 will coincide with the principal section of crystal 7. Therefore, in both divided ray bundles, the difference in location between the.

focus points of the paraxial rays for the observed incident plane in system 10 has the opposite sign to that of system 9. The resulting difference in position is, therefore, zero and the extent of the image spots of each of the two divided ray bundles is considerably reduced after the two divided ray bundles have passed through the A/Z-thin plate 8 and the system 10.

The correction of the path length difference between the ordinary and extraordinary divided ray bundles is achieved in system 10 by crystal 12 in the same way as has been described for system 9.

Because of the considerable reduction in the extent of the image spots of each of the two divided ray bundles, the distance of the two image spots, i.e., the magnitude or size of the light deviation can be reduced. As this distance is in proportion to the thickness of crystals 6, ll, 7, 12, this thickness can, therefore, also be refuced. Through this reduction there can be achieved a further reduction of the extent of the two image spots as the extent of the image spots is also in proportion to the thickness of crystals 6, 11,7, 12.

The embodiment according to H08. 4 and 5 causes in comparison with a known uncorrected system having the same crystal thickness a IT fold light deviation as in systems 9 and [0 the light deviations are perpendicular to each other. If this increase in the light deviation is not desirable, then the increase can be avoided by reduction of the thickness is of the doubly refracting crystals 6, l1, 7, 12 by FIG. 6 shows a light deflection system of two stages in one dimension. An essential element of this light deflection system is the system of doubly refracting crystals, described in the FIGS. 1 to 5. The parallel light beam of a laser is focused with an objective 19 onto the photographic plane 18. The polarization-dependent refraction in doubly refracting crystals 6, ll, 7, 12 is used for the deflection of the light beam. The electro-optic switches 17 can switch the collimated light beam completely from one linear polarization state to an orthogonal polarization state. Two orthogonal polarizations are obtained by applying either no voltage, or the half-wave voltage. When both switches 22 and 24 are opened the focal point is in point 22. When the switch 23 is opened and switch 24 is shut, then the light beam is focused to point 21. Four different focal points exist for this light deflection system.

The same difference between the focal points 22 and 21 can be achieved, when the systems 10 and the A/2-thin plate are omitted and the length of the crystals 6 and 11 is increased to V2. In this case the image spots produced for each light ray bundle are increased too from theapertural defect lhelnage spots are overlapped. In order to arrive at a situation wherein the image spots are not overlapped, the apertural error must be reduced in the same way as described in FIGS. 1 to 5. In the example given in FIG. 6 the apertural error will be reduced in analogy to FIGS. 4 and 5.

SUMMARY OF EQUATIONS 1. An arrangement of doubly refracting crystals for the reduction of aperture defects, comprising a first doubly refracting crystal and a second doubly refracting crystal of the same geometrical form but having the opposite sign of double refraction, wherein the optical axis of said second crystal is in the plane of the system axis and the optical axis of said first crystal, said first and second crystals having the parameters of ordinary refractive indices n and n respectively, extraordinary refractive indices n, and n, respectively, thicknesses d, and d respectively, and angles y, and y, between said system axis and the optical axes respectively, and wherein said parameters have values whereby the path length difference of the paraxial rays of the extraordinary divided ray bundle for the principal section equals the path length difference for the 3. The arrangement of claim 1 wherein said parameters have values whereby the intercept length of the paraxial rays of the ordinary divided ray bundle equals the intercept length of the paraxial rays of the extraordinary divided ray bundle of the principal section.

4. The arrangement of claim 3 wherein:

G =n sin y n2 cos 7 5. The arrangement of claim 1 wherein said doubly refracting crystals are planoparallel plates.

* a: k a:

} UNITED STATES PATENT OFFICE CERTIFICATE OF' CORRECTION Patent: No. 316441018 D t d February 22, 1972 l flg) Giinter Pasold It. is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

IN THE SPECIFICATION:

' 2 2 2 II I. +n .cos Y Column 6, line 13, change G n sln Y e1 1 2 2 2 2 .sin +n to G1 n 01 81 Y IN THE CLAIMS:

Claim 4, second equation, change 2 2 n 2 2 2 sin Y +n cos Y to --G =n sin Y +11 COS Y 1 ol 1 e1 1 l 01 l 01 l Signed and sealed this 6th day of June 1972.

(SEAL) Attest:

EDWARD M.FLETCHER, JR. ROBERT GOTTSCHALK Commissioner of Patents At-testing Officer USCOMM-DC 6O376-P69 us, GOVERNMENT PRINTING OFFICE: I989 O366334 FORM PO-IOSO (10-69) 

1. An arrangement of doubly refracting crystals for the reduction of aperture defects, comprising a first doubly refracting crystal and a second doubly refracting crystal of the same geometrical form but having the opposite sign of double refraction, wherein the optical axis of said second crystal is in the plane of the system axis and the optical axis of said first crystal, said first and second crystals having the parameters of ordinary refractive indices n01 and n02 respectively, extraordinary refractive indices ne1 and ne2 respectively, thicknesses d1 and d2 respectively, and angles gamma 1 and gamma 2 between said system axis and the optical axes respectively, and wherein said parameters have values whereby the path length difference of the paraxial rays of the extraordinary divided ray bundle for the principal section equals the path length difference for the section perpendicular to the principal section.
 2. The arrangement of claim 1 wherein: where G1 n201 sin2 gamma 1 + n2e1 cos2 gamma 1 and G2 n2o2 sin2 gamma 2 + n2e2 cos2 gamma 2
 3. The arrangement of claim 1 wherein said parameters have values whereby the intercept length of the paraxial rays of the ordinary divided ray bundle equals the intercept length of the paraxial rays of the extraordinAry divided ray bundle of the principal section.
 4. The arrangement of claim 3 wherein: where G1 n2o1 sin2 gamma 1 + n2o1 cos2 gamma 1 and G2 n2o2 sin2 gamma 2 + n2e2 cos2 gamma 2
 5. The arrangement of claim 1 wherein said doubly refracting crystals are planoparallel plates. 